Combine bread flour, instant yeast, salt, and sugar in a stand mixer bowl. Add the slightly warmed applesauce and oil. Mix on low with a dough hook for 1 minute, then increase to medium and knead for 8-10 minutes until smooth and elastic.
Place dough in a lightly greased bowl, cover, and let rise in a warm spot for about 1 hour or until doubled in size.
Shape and Fill
Punch down the dough and roll out on a floured surface into an 18x10 inch rectangle.
Spread the softened butter evenly over the dough. Mix the brown sugar and cinnamon together, then sprinkle evenly over the butter.
Roll the dough tightly starting from one long edge. Pinch the seam to seal. Cut into 12 even rounds using a sharp knife or dental floss.
Place the rolls cut-side up in a greased 9x13 inch baking pan. Cover and let rise for 30 minutes until puffy.
Bake and Frost
Preheat oven to 350°F. Bake rolls for 20-22 minutes until golden brown on top.
While rolls bake, beat together the softened cream cheese, powdered sugar, cinnamon, and vanilla until smooth and fluffy.
Let rolls cool for 5 minutes, then spread frosting generously over the warm rolls. Serve immediately.
Notes
Overnight method: After placing rolls in the pan, cover tightly with plastic wrap and refrigerate up to 18 hours. Remove, let sit 30 minutes at room temperature, then bake as directed.
Applesauce temperature: Warm it to about 110°F (warm to touch, not hot) to help activate the yeast.
All-purpose flour substitute: You can use all-purpose flour for softer rolls with less chew. The dough may be slightly stickier.
Vegan option: Use vegan cream cheese and plant-based butter. The dough itself is nearly vegan.
Storage: Unfrosted rolls keep at room temperature 3-4 days. Frosted rolls should be refrigerated and consumed within 5 days. Freeze unfrosted rolls up to 3 months.